Haha nice one...a bit similar to the way that Dumbledore mimics Gandalf, no?
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Not to mention the obvious Ringwraith-Dementor connection..."Radagast is, of course, a worthy wizard, a master of shapes and changes of hue, and he has much lore of herbs and beasts, and birds are especially his friends."-Gandalf, The Lord of the Rings.

I seem to remember he can disappear and reappear and do some magic - the extent of im not too sure but i think its quite powerful. If he can then that would beat gollum who is more just fairly strong in the physical sense.

Dobby has the advantage if he is allowed to use his magic. But Gollum could still level the playing field.

DOBBY: and now I will jinx you with...why are you crying? GOLLUM: Smeagol didn't do it. It was the precioussss! DOBBY: I don't trust you. You tried to strangle me in my sleep. Now I'm still going to hex you. GOLLUM: The precioussss made us do it. We gives House Elf a birthday present, yesss. DOBBY: It isn't my birthday. What sort of present? GOLLUM; This way, come see. More recruitses for "SSssSPEWunionses"? DOBBY Society for Promotion of Elvish Welfare. SPEW. GOLLUM. Gessssundheit....Fresh meats... recruitses, we means. DOBBY: Really? You don't say? Where might these.... GOLLUM: Smeagol shows the way! Smeagol always helps! First the... secret stair..... DOBBY: secret stair..... GOLLUM: then through a.... a tunnel.... DOBBY: sounds dangerous. GOLLUM: There is no other way. Either go Smeagol's way... or go back. DOBBY: I can just apparate there. Just tell me where. GOLLUM: Right inside that tunnel up there. Then one left, yes. Then two rights, yes yes. DOBBY: i can't see it from down here. GOLLUM: We shows house Elf. Look at mapssss. DOBBY: you have a map? (Leans closer) (GOLLUM seizes DOBBY suddenly, puts him in a grappler's chokehold.) GOLLUM: Naughty little fly. Why does it cry? Caught in a web. Soon to be.... (Takes a bite of some House Elf sushi) .... eaten! A bag is like a hole that you can carry with you.

It would be a good fight especially is Gollum still had the the ring. If he didn't then I would chose Dobby because he can use magic, which is a bit unfair. But if it was hand to hand and no magic the Gollum would easily win. He's been slayin midgets for centuries!

Devious, plus that killer instinct and close-combat skills. Dobby's magically powerful, but can't use it if he's too busy being strangled and then bitten. A bag is like a hole that you can carry with you.

he'd just disapparate. Plus he can handle pain, he is into self-punishment after all. Gollum would need to strike him over the head with a rock, knock him unconscious, see, then he can eats him whole. Here's a train of thought I never thought I'd have.

Dobby does have at least a chance of being able to Disapparate or some other magic, as you suggest. You are right about that.

Gollum might be able to prevent that, or lessen the likelihood, by executing the hold with sufficient technique and with surprise. A grappler's chokehold involves the use of all four limbs to tie up the opponent, for proper positioning before attempting the choke (in Brazilian grappling arts, the maxim is "position before submission" . In TTT, Gollum uses a technique known to the Brazilians as "rear naked choke" on Sam-foiled only by Frodo, threatening Gollum with Sting.). Dobby might be too constricted, and too busy panicking from having his blood and air supply being cut off, that he might not even be able to snap his fingers, or mentally focus enough to do the necessary magic. Although he is used to self-inflicted punishment, being on the receiving end by another, by surprise, is different- there is an element of shock involved, especially for those untrained in close combat. Dobby has zero close-combat experience, or at least has exhibited none. I don't think anyone in the Harry Potter stories is known to have any experience with non-magical combat. I think Dobby would be quite shocked at being physically assaulted by a seasoned, bloodthirsty killer, pain-resistant or not.

You're right about using a rock, it would be more likely to prevent Dobby from using magic than a choke attempt. Gollum is quite skilled at that. I'll go with that. A bag is like a hole that you can carry with you.

I was curious though, about what you meant that it might not be considered much of a victory? you mean morally speaking? Surely Dobby would be a sufficiently worthy opponent...? A bag is like a hole that you can carry with you.

Dobby was used to being on the receiving end of physical assaults - from the Malfoys. He has long experience with torture, sudden attacks, and devious behavior. This contest is far from a slam-dunk for either being! Walk to Rivendell: There and Back Again Challenge - getting thirteen rowdy Dwarves, one grumpy Wizard, and a beleaguered Hobbit from Bag End to the Lonely Mountain by December 2012; and the same Hobbit and Wizard back to Bag End by December 2013

First: Something about Dobbie and socks ... I don't know the HP universe all that well ... but for some reason he seems to depend on them in a way that could be exploited to Gollum's advantage ... maybe?

Second: The element of surprise. Is this a fair and official fight in an arena or something? Or do they encounter each other in some dark cave somewhere? The first gives the advantage to Dobbie and the second to Gollum.

A fight between Gollum and Dobby would be an unwinnable stalemate. Gollum is devious enough that he could probably succeed in tricking Dobby, but Dobby could vanish from a chokehold or the flight-path of a rock. He can make objects fly (notably Aunt Petunia's pudding and the rogue bludger that he caused to attack Harry), so he might even be a better shot/harder thrower with a rock than Gollum would be. The bludger he set on Harry did not desist until it was physically locked up (if that counts as desisting; it didn't give up), so he could quite conceivably enchant a rock to follow/chase Gollum and whack him repeatedly for eternity. However, Dobby would be too softhearted to go for a killing blow (unless perhaps Gollum was threatening someone he cared about) whereas Gollum would pull no punches . . . aaaand we're back where we started, with Dobby vanishing from any finishing move Gollum may attempt.

I think Dobby would have to win. In Harry Potter, house elfs are supposed to be quite powerful in magic and Dobby even defeated Lucius Malfoy. I do not think Gollum could match Dobby's magic powers and even though I wish Gollum would win just because I like seeing the LOTR characters winning, I do not think Gollum would be able to pull it off.

magically attacks Lucius Malfoy, blasting him down a flight of stairs. In another scene he uses magic to drop a large chandelier onto Bellatrix Lestrange. He can enchant inanimate objects to float, or to attack people. He can Disapparate (magically move from one place to another). And he can create impassable magical barriers. House Elves fight in the HP series' final battle. (Dobby does not, as he is not around to do so).

Unless Gollum has the Ring, I would say Dobby would win. He is a (by Potterverse standards) reasonably powerful magic user who cannot be disarmed (House Elves do not use wands), and is skilled in using his magic to move objects, even large ones/animate ones, which could be used to knock Gollum unconscious. I agree with those who suggest Dobby would be inclined to spare Gollum's life, but I would consider a knockout after which Dobby Disapparates, a Dobby win.